Honors Projects in MathematicsCopyright (c) 2016 Bryant University All rights reserved.http://digitalcommons.bryant.edu/honors_mathematics
Recent documents in Honors Projects in Mathematicsen-usThu, 01 Sep 2016 01:47:03 PDT3600The Evaluation of Rhode Island Public High School Teachers: The Impact on Studentshttp://digitalcommons.bryant.edu/honors_mathematics/27
http://digitalcommons.bryant.edu/honors_mathematics/27Tue, 30 Aug 2016 11:38:11 PDT
In 2012, the state of Rhode Island began the full implementation of a high-stakes teacher evaluation system. Its purpose is to increase teacher accountability and to improve student performance. However, a significant amount of literature casts doubt about the effectiveness and validity of teacher evaluation. This paper utilizes statistical methods including regression and decision trees in order to determine whether or not there is a relationship between teacher evaluation in Rhode Island and student performance, using RI Department of Education Data for each school from 2008-2015. Furthermore, this presentation investigates other factors that affect schools, to see if changes in student performance can be explained by factors other than the teacher evaluation system, such as discipline, the student-teacher ratio, and student demographics.
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Stephen LamontagneMathematicsSecondary educationEducation policyCatching Card Countershttp://digitalcommons.bryant.edu/honors_mathematics/26
http://digitalcommons.bryant.edu/honors_mathematics/26Tue, 30 Aug 2016 09:22:54 PDT
The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. Conversely, the unpredictable betting strategy of a “normal” gambler was gathered through observations of over one thousands hands of blackjack. The comparison of the two led to deviations in behavior and betting habits. An understanding of these differences will provide a casino with additional information to catch card counters at the table.
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Sarah FrenchMathematicsComputer scienceBehavioral sciencesWhat is the True Cost to stay in the Hospital?http://digitalcommons.bryant.edu/honors_mathematics/25
http://digitalcommons.bryant.edu/honors_mathematics/25Tue, 30 Aug 2016 09:07:49 PDT
Currently, the unfortunate reality that receiving diverse health procedures can be extremely expensive is widely acknowledged and woefully accepted. However, have you inquired or been curious about the specific factors that influence the cost per day expensed by a hospital? Through examination, investigation, and evaluation operating SAS Enterprise Guide, SAS Enterprise Miner and Tableau I have attempted to arrive at a conclusion for this very question. Utilizing a 1.5 million row data set provided by Rhode Island, for the years 2003-2013, I analyzed the assorted elements conceivably bearing impact on the cost per day at a hospital. Regressions, decision trees, neural networks, ANOVA, linear models, and a countless number of visual representations genuinely assisted in attaining a robust conclusion. Overall, a number of various input variables, with unique magnitudes, such as age, services provided, year of discharge, and hospital provider sincerely shape the overarching cost per day at a hospital.
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Samantha AlicandroHealth careMathematicsPredictions of Success in the Actuarial Majorhttp://digitalcommons.bryant.edu/honors_mathematics/24
http://digitalcommons.bryant.edu/honors_mathematics/24Fri, 26 Aug 2016 09:44:18 PDT
This study finds predictive factors that have a significant effect on the ending Mathematics/Actuarial GPA of Actuarial majors at Bryant University. This was done to add clarity to incoming students for what it takes to do well in the actuarial major. There were 266 subjects consisting of Bryant students that graduated between the years 2009 and 2015. The data was received in the form of final transcripts upon graduation for these students. Through manipulation of these transcripts, GPAs were calculated for Mathematics/Actuarial, English/Literary Cultural Studies, History/Politics, Economics, Science, Social Sciences, Computer Information Systems, Finance, Accounting, Management, and Marketing. These GPAs were found after 2 years (4 semesters) of classes and also after 3 years (6 semesters) of classes to see if the predictive factors differ between the two years. I also ran models comparing just the Arts and Sciences as well as just the business to see how the results differ using just those subjects rather than putting them all together. I used regression and decision trees in order to generate results. In order to use regression, I needed to impute missing values with SAS Enterprise Miner 13.2 to use all of the data. I did this using the tree surrogate method to accurately impute the data. I did not include Mathematics/Actuarial in these predictive models because of the high correlation to the final Mathematics/Actuarial GPA that I am trying to predict. After comparing the different models, English, Computer Information Systems, and Economics were the highest predictors after two years and Finance English and Science were the highest predictors after three years.
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Jessica SoojianMathematicsThe Effect of Tommy John (UCL) Reconstructive Surgery on a Pitcher’s Arm and Career Progressionhttp://digitalcommons.bryant.edu/honors_mathematics/23
http://digitalcommons.bryant.edu/honors_mathematics/23Fri, 26 Aug 2016 09:10:50 PDT
Injuries have plagued professional athletes since their sports have been in existence. The examination of how teams can diminish the side effects of the injuries en route to a speedy recovery remains an evolving process and a topic of concern for all. Injury preventative tactics have been implemented by coaching staffs and various training personnel. Major League Baseball (MLB) pitchers are noticing an increase in the number of surgeries performed each year. The tearing of the ulnar collateral ligament (UCL) in the elbow has become a predominant injury among pitchers in the MLB. Reconstructive surgery, also known as Tommy John surgery, has been a necessity for any pitcher wishing to return to the mound. The goal of this research is to examine performance of players who elect to undergo Tommy John surgery. The development of a predictive model can only go so-far to include factual statistical data to determine the stress of pitchers’ arms. However, the byproducts of teams acquiring this knowledge has a large impact on their decision making abilities. The research includes analytical techniques to predict future outcomes of MLB pitchers as well as an avenue to provide statistical evidence of the before and after effects on their arms.
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Jack GrantMathematicsProfessional sportsHealth careStandardized Testing: What is it Good For? A Case Study in Connecticuthttp://digitalcommons.bryant.edu/honors_mathematics/22
http://digitalcommons.bryant.edu/honors_mathematics/22Wed, 22 Jul 2015 07:23:02 PDT
The case study was developed in an attempt to shed more light on the debate of standardized testing. The goal of the study was to find evidence to support whether or not standardized testing is worth doing in public secondary schools. To investigate this question, the state standardized math test scores of three Connecticut public high schools were analyzed. The average math scores over thirteen years were observed and statistical analysis was performed to see if any significant differences existed between the three schools. Tests were performed before and after the change in standardized test. The graduation rates of the schools were observed and compared to the trend of the CAPT mean math scores over time. This analysis was then supplemented with responses from a survey distributed to Connecticut high school math teachers to take into consideration the educators’ views of standardized testing. Both the quantitative and qualitative data had conflicting results. The standardized test scores appeared to improve over time, while the teachers found their teaching and student learning was interfered with the testing. Following the analyses, future implications of using standardized testing and how it may affect the transition to the Common Core Standards is discussed. - 1
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Megan MappMathematicsSecondary educationEducation policyThe Implications of Self-Driving Cars on Insurancehttp://digitalcommons.bryant.edu/honors_mathematics/21
http://digitalcommons.bryant.edu/honors_mathematics/21Wed, 22 Jul 2015 06:53:46 PDT
Self-driving cars, also known as autonomous vehicles, are being researched and tested by automakers, technology industry leaders, and other institutions. Lawmakers and politicians are discussing the legislation that will affect the fate of such technology. Primary benefits include safety, mobility, free time, less traffic, and green effects. However, there are also obstacles to the implementation of self-driving vehicles including consumer acceptance, legal liability, and cost. With the potential shift in responsibility from driver to automaker, rating factors for insurance may change, weighing more heavily on the model of the car as a factor. The fate of auto insurance is in the demand for autonomous vehicles by consumers, as business leaders react on data, not ideas. This project measures demand for self-driving cars and applies the results to how auto insurance will change. A survey was distributed in order to determine students’ experience with car insurance and their attitudes on self-driving technology. The survey group is divided between general students and those with some insurance knowledge. By using the demand findings from the survey as well as existing data for older driver populations, we are better able to predict the demand and liability of self-driving cars and how auto insurance will be priced.
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Amanda LoBelloMathematicsBehavioral sciencesCorporate liabilityEconomic policyEnergy policyEnvironmental policyMathematical Modeling of Trending Topics on Twitterhttp://digitalcommons.bryant.edu/honors_mathematics/20
http://digitalcommons.bryant.edu/honors_mathematics/20Wed, 22 Jul 2015 05:27:57 PDT
Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses information spread, presents case studies pertaining to the prevalence of several “trending” topics on Twitter over time. The study introduces a framework to compare information dynamics on Twitter based on the topical area as well as a framework for the prediction of topic prevalence. Additionally, methodological and results-based comparisons are drawn between the spread of information and the spread of infectious disease.
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Jonathan S. SkazaInformation technologyMathematicsSocial conditions & trendsDoes Being Bilingual Make You Better At Math?http://digitalcommons.bryant.edu/honors_mathematics/19
http://digitalcommons.bryant.edu/honors_mathematics/19Tue, 21 Jul 2015 12:28:52 PDT
The purpose of this study is to examine if there is any relationship between being bilingual, defined as speaking your native language at home and another language in school, and your mathematical ability. Data from the National Longitudinal Study of Adolescent Health was used to compare the math grades of students who were not born in the US and speak English, Spanish, or Other at home. Also, data from the Bryant University first year students was used to test if students who speak a different language at home have a higher mathematical average than their monolingual peers. Results show that students who are classified as balanced bilinguals perform better at math than monolingual or one-dominant bilingual students.
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Enxhi EleziMathematicsLanguageBootstrapping vs. Asymptotic Theory in Property and Casualty Loss Reservinghttp://digitalcommons.bryant.edu/honors_mathematics/18
http://digitalcommons.bryant.edu/honors_mathematics/18Tue, 21 Jul 2015 07:59:06 PDT
One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling distribution of the reserve estimates; and asymptotic theory, which resamples only the GLM parameters (fitted from an original set of data) from a multivariate normal distribution to estimate the sampling distribution of the reserve estimates. Using Excel, R, and SAS software, the copulas of the GLM parameter estimates from the stochastic methods will be compared to the copula from a multivariate normal distribution. Ultimately, the Value at Risk (VaR) and Tail Value at Risk (TVaR) results from each method’s sampling distribution will be compared to each other, with the goal of showing that the two methods produce significantly different reserve estimates and risk capital estimates at the low end of the reserve distribution. This would answer the question as to whether the asymptotic theory procedure sufficiently approximates real-world scenarios.
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Andrew J. DiFronzo Jr.MathematicsActive vs. Passive Portfolio Managementhttp://digitalcommons.bryant.edu/honors_mathematics/17
http://digitalcommons.bryant.edu/honors_mathematics/17Wed, 09 Jul 2014 08:49:20 PDT
In the finance community there is a huge debate about whether or not active portfolio managers can provide better returns than passive managers. While active managers often provide excess returns, the costs of running an active fund offset whatever gains were made in the market. The objective of this report is to figure out whether or not active funds provide larger returns than passive funds on a cost adjusted basis. This report will identify which type of fund is a more cost effective investment, as well as identify different properties of funds and how they operate. The goal of doing this research is to provide information to the average investor, rather than a multi-millionaire, about what kind of fund may be more appropriate for them to invest in. To successfully complete this project I collected quantitative fund data from fidelity, and qualitative information from various finance and business journals. After running a multivariate analysis of variance on my data I found that passive funds in the 1 year period provided significantly greater returns than active funds on a cost adjusted basis. Next, over the 3 year period, there was no significant difference between the returns of active and passive stock funds. However, during the 5 year period return active funds proved to be a more cost effective investment strategy. From my results I have concluded that active portfolio management is not a more cost effective investment tool than passive management.
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Timothy GreenhillMathematicsRelationship between Classroom Climate, Student Self-Efficacy, and Achievement in the High School Math Classroomhttp://digitalcommons.bryant.edu/honors_mathematics/16
http://digitalcommons.bryant.edu/honors_mathematics/16Mon, 30 Jun 2014 06:32:36 PDT
There is a variety of past research regarding the relationship between the mathematics classroom climate and student learning. More specifically, many studies look at how the classroom climate may influence student self-efficacy in math. Furthermore, another quantity of research supports that there is a link between student math self-efficacy and the student’s achievement in the particular subject. The goal of this study is to see if students’ perceptions of their math classroom climate are related to their self-efficacies towards the subject, which therefore affects their achievement in math. It is hypothesized that there is a relationship between the classroom environment and student self-efficacy; furthermore, it is hypothesized this relationship contributes to student achievement in math. Participants were 83 high school students attending a public suburban school outside of Boston in the winter of 2014. Students completed Fast’s measure assessing classroom climate, math self-efficacy and achievement. A significant relationship was found between classroom climate and student self-efficacy, with mastery goal structure being the most significant aspect of classroom climate that contributes to this relationship. A significant relationship was found between self-efficacy and achievement, but boys had higher self-efficacies while girls had higher achievement.
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Delaney CarrMathematicsThe Impact of Professional Sports Franchises on Local Economieshttp://digitalcommons.bryant.edu/honors_mathematics/15
http://digitalcommons.bryant.edu/honors_mathematics/15Fri, 27 Jun 2014 09:30:38 PDT
There is no doubt that professional sports franchises and stadiums generate a significant amount of economic activity, but is the impact on the local economy positive, negative, or neutral? Studies have shown that, while franchises can give the economy a boost in the short term, there are little to no long-term positive effects. This capstone will examine the trend in public financing of stadiums, look at the impact of stadium location, explore the factors of the economy that are impacted by professional sports franchises, and determine if the effects vary by sport or by region. Several major case studies will be examined to provide specific examples, including the most recent Super Bowl in New Jersey. Once the literature review is complete, regression analysis will be used to make an ultimate conclusion on the value of professional sports franchises and stadiums in the United States and the optimal location in which to start a new professional sports franchise in the United States. This will be done using data from 2001-2012 and variables that have been proven to have an impact one way or another. The result will be a prediction of the type and location of the next professional sports franchise in the United States.
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Jeffrey PierroMathematicsInternet Radio: An Analysis of Pandora and Spotifyhttp://digitalcommons.bryant.edu/honors_mathematics/14
http://digitalcommons.bryant.edu/honors_mathematics/14Fri, 27 Jun 2014 09:20:29 PDT
Unlike traditional stations, internet radio stations try to complete the task of effectively

identifying the individual in their audience and then cater to their musical taste. The

effectiveness of these stations can be analyzed through popular music customization mediums,

such as Pandora and Spotify. This paper seeks to analyze Pandora and Spotify and research

why they are such popular mediums for their users and how effective each site is in satisfying

a need for personalized radio. Specifically, what medium used for internet radio best caters

to the needs of users in terms of website features (extent of personalization and social media

integration), availability of services (access and costs), and music appreciation features

(quality, content and variety)? This paper highlights what qualities users value most of

Pandora and Spotify. Two experiments are performed, one is objective (self-conductive) and

the other is subjective (with a group of college age listeners) which answers the question:

when both mediums are given the same parameters how do their performances differ? There

is a survey associated with the subjective experiment where users provide demographic

information and rank certain features based on their performance. Although neither station

significantly outperformed the other in terms of the subjective experiment, many of the

differences between the two services are highlighted throughout the paper.

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Corinne LoiaconoMathematicsActual vs. Perceived Value of Players of the National Basketball Associationhttp://digitalcommons.bryant.edu/honors_mathematics/13
http://digitalcommons.bryant.edu/honors_mathematics/13Mon, 01 Jul 2013 18:14:32 PDT
Over the past few decades the media has played an increasingly large role in shaping how player effectiveness in the National Basketball Association (NBA) is perceived. Several factors have caused fans, announcers, and even NBA team management to have unintentional bias toward certain players. This study aims to utilize various formulas created by NBA statisticians, called Player Raters, to identify how efficient each NBA player actually is in comparison to the rest of the league. Data from the past 12 seasons was compiled and six Player Raters were used to place values on every NBA player since the 2000-2001 season. MVP voting results for these seasons were also gathered and used to quantify how the public perceives the effectiveness of the top players in the NBA. Correlation tests between Player Rater and MVP voting results revealed players who were overrated because of various “perception factors”. A single formula combining the six raters used in this study was also developed. Clearly the application of statistics to NBA data used in this study will be useful to all NBA audiences. It will help fans and announcers become aware of their unintentional bias when judging player effectiveness and also NBA team managers when making important decisions like trades, salary negotiations, and allotting playing time.
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Stephen RighiniProfessional sportsMathematicsThe Stock Market Impact of Bond Rating Changeshttp://digitalcommons.bryant.edu/honors_mathematics/12
http://digitalcommons.bryant.edu/honors_mathematics/12Mon, 01 Jul 2013 12:20:26 PDT
This paper examines the impact of a downgrade of a company’s credit rating on its stock price in the days surrounding the downgrade. If we consider this downgrade new information, then a negative impact on the company’s stock price would be expected. However, if we assume that rating agencies use information that investors have already accounted for, then there would be no impact. There could also be an impact, at least temporarily, due to the fact that a ratings downgrade is bad news, even if the reasons for the downgrade have already been priced in. To perform this analysis I used an event study, a technique commonly used in finance to identify the impact of one event on a particular variable. I discovered that no statistically significant abnormal returns exist on the day of a ratings downgrade, and on the days surrounding it. The information content of a downgrade to equity investors is low as the information resulting in the downgrade has already been reflected in the company’s stock price.
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Michael LeonardMathematicsTime Series Data Mining: A Retail Application Using SAS Enterprise Minerhttp://digitalcommons.bryant.edu/honors_mathematics/11
http://digitalcommons.bryant.edu/honors_mathematics/11Sun, 30 Jun 2013 14:52:56 PDT
Modern technologies have allowed for the amassment of data at a rate never encountered before. Organizations are now able to routinely collect and process massive volumes of data. A plethora of regularly collected information can be ordered using an appropriate time interval. The data would thus be developed into a time series. With such data, analytical techniques can be employed to collect information pertaining to historical trends and seasonality. Time series data mining methodology allows users to identify commonalities between sets of time-ordered data. This technique is supported by a variety of algorithms, notably dynamic time warping (DTW). This mathematical technique supports the identification of similarities between numerous time series. The following research aims to provide a practical application of this methodology using SAS Enterprise Miner, an industry-leading software platform for business analytics. Due to the prevalence of time series data in retail settings, a realistic product sales transaction data set was analyzed. This information was provided by dunnhumbyUSA. Interpretations were drawn from output that was generated using “TS nodes” in SAS Enterprise Miner.
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Daniel HebertInformation technologyMathematicsWho Is The American League MVP On a Per Dollar Basis?http://digitalcommons.bryant.edu/honors_mathematics/10
http://digitalcommons.bryant.edu/honors_mathematics/10Tue, 18 Jun 2013 17:34:40 PDT
This study will look at the value of MLB players in the American League on a per dollar basis. It will be based on the 2011 statistics and will use a linear regression model to create a value for each player. The value will be based on a variety of statistics based upon position. For all players: age, team wins, and years in the league will be accounted for. For field players: games played, hits, runs, doubles, triples, home runs, runs batted in, walks, strike outs, stolen bases, on base percentage, slugging percentage, fielding percentage and errors will be accounted for as well. Pitchers will be based on stats on a per inning basis of: innings, strike outs, walks, earned run average, walks hits per inning pitched, quality starts, saves and wins above replacement. The general public sees players as stars based on their giant contracts, and who is paid the most. There are players in the league who play better on a per dollar basis that the famous stars who have massive contracts. I will discover who those players are.
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Patrick DeckerMathematicsProfessional sportsA Study of Women Working in the Actuarial Fieldhttp://digitalcommons.bryant.edu/honors_mathematics/9
http://digitalcommons.bryant.edu/honors_mathematics/9Mon, 25 Mar 2013 20:48:18 PDT
The goal of this project is to examine how women fit into the actuarial career path and how cultural expectations, biological factors, and personal aspirations affect their experiences in the field. Dramatic changes in the profession have occurred since its emergence in the nineteenth century to become more welcoming to women who choose to enter the profession. However, despite the equalizing demographic shifts of the field, it is still a male-dominated profession. This paper attempts to analyze why some of the changes in the demographics of the field have occurred as well as explain what factors contribute to women’s underrepresentation as actuarial professionals by referring to previous research regarding gender roles in mathematics, which arguably arise from both biological and sociological sources. To help tie these arguments into the specific field of actuarial mathematics, an independent survey was administered to current and former actuaries that tested their beliefs about the degree to which gender can influence success in the actuarial field, and the results were compared to existing theories about women in mathematics. The survey participants were selected using the names from the online data base ActuarialDirectory.org as well as using a list of Bryant Alums who graduated with a degree in Actuarial Sciences that was provided from Bryant’s Alumni Network. The test results were analyzed using two tail t-tests, and further detail about the testing processes can be found in appendix C.
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Jillian EmbergGender studiesMathematicsAre NFL Athletes Receiving Over-Valued Contracts?http://digitalcommons.bryant.edu/honors_mathematics/8
http://digitalcommons.bryant.edu/honors_mathematics/8Sun, 24 Mar 2013 20:48:55 PDT
Many sport research studies have been conducted that examine the performance of professional athletes and their corresponding effect on franchise winning percentages, team revenues, economic repercussions, performance-based compensation, and much more. Research in the National Football League, however, has been found to be somewhat limited due to the numerous possible positions and resulting vastness of position-specific variables. The NFL lockout in 2011 caused many to question the specific relationship between professional athlete performance and salary distribution. This study’s purpose was to find a collection of variables with which all NFL athletes could be compared, and to identify relationships existing between a player’s performance and his value/salary. Data was collected from USAToday.com, Pro-football-reference.com, and AdvancedNFLStats.com. This data was then organized and manipulated into a format that allowed all players in the league during the 2009 season to be compared. Of the nine variables considered for this study, four were found to have a significant relationship with a player’s value/salary. These results were utilized to create a Player Valuation model and then analyze the overall salary distribution throughout the NFL. From this, it was observed while there are many athletes in the NFL that receive extravagant salaries well over their projected value, there is a much larger portion of the league that is undervalued and receive less than their projected value. It was then concluded that a super-star variable would be necessary to create a more accurate Player Valuation model, and the reason there is a larger proportion of NFL players receiving a lower salary than they deserve is due to franchise cap limits. These cap limits place pressure on franchises to push down the salaries of non-superstar athletes in order to compensate for the salaries required for the super-star athletes on their rosters.
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Jason ScottMathematicsProfessional sports